An adaptive, rate-optimal test of a parametric mean-regression model against a nonparametric alternative
An adaptive, rate-optimal test of a parametric mean-regression model against a nonparametric alternative
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DOI：
10.1111/1468-0262.00207
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发表时间：
2001-05-01
期刊：
影响因子：
6.1
通讯作者：
Spokoiny, VG
中科院分区：
文献类型：
--
作者：
Horowitz, JL;Spokoiny, VG
我们开发了一个新的测试的参数模型的条件均值函数对非参数的替代。该测试适应于备选模型的未知平滑度，并且一致地一致反对其与参数模型的距离以最快可能的速率收敛到零的备选方案。这个速率比n（-1/2）慢。一些现有的测试有非平凡的权力对限制类的替代品，其距离参数模型的减少率n（-1/2）。然而，有一些替代品的序列，这些测试是不一致的，而我们的测试是一致的。因此，有替代模型，我们的测试的有限样本功率大大超过现有的测试。一些Monte Carlo实验的结果说明了这一结论。
We develop a new test of a parametric model of a conditional mean function against a nonparametric alternative. The test adapts to the unknown smoothness of the alternative model and is uniformly consistent against alternatives whose distance from the parametric model converges to zero at the fastest possible rate. This rate is slower than n(-1/2). Some existing tests have nontrivial power against restricted classes of alternatives whose distance from the parametric model decreases at the rate n(-1/2). There are, however, sequences of alternatives against which these tests are inconsistent and ours is consistent. As a consequence, there are alternative models for which the finite-sample power of our test greatly exceeds that of existing tests. This conclusion is illustrated by the results of some Monte Carlo experiments.